Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 5: Problem 33

An atom in an excited state can drop to a lower energy state by emitting a photon. Is it possible to predict exactly how long the atom will remain in the higher energy state? Explain your answer.

Short Answer

Expert verified
It is not possible to predict exactly how long an atom will remain in the higher energy state due to the statistical nature of decay and the Heisenberg uncertainty principle.

Step by step solution

01

- Understand the quantum mechanics basics

In quantum mechanics, an excited atom can drop to a lower energy state by emitting a photon. This process is called spontaneous emission.
02

- Introduce the concept of decay time

The time an atom spends in an excited state before emitting a photon is referred to as the decay time or lifetime of the excited state.
03

- Nature of decay time

Decay time is not a fixed value for an individual event. Instead, it's statistically distributed according to an exponential decay law, meaning we can only predict the average time an ensemble of atoms will take to decay, but not for an individual atom.
04

- Heisenberg uncertainty principle

The Heisenberg uncertainty principle indicates that there is a fundamental limit to the precision with which energy states and time duration of an excited state can be known. Thus, exact prediction of an atom's lifetime in an excited state is impossible.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

spontaneous emission
In quantum mechanics, atoms have different energy levels. When an atom is in an excited state, which means it has more energy than its ground state, it can drop to a lower energy level by releasing energy in the form of a photon. This process is known as spontaneous emission. This emission happens without any external influence, purely due to the inherent properties of the atom.
  • Photon emission is random.
  • It contributes to phenomena such as fluorescence and lasers.
Understanding spontaneous emission is fundamental to grasping more complex quantum phenomena.
exponential decay
The concept of exponential decay is crucial to understanding how long an atom remains in an excited state before emitting a photon. The decay time, or lifetime of an excited state, does not follow a fixed timeline. Instead, it follows an exponential decay law. This means:
  • The probability that an atom will emit a photon decreases exponentially over time.
  • On average, a large number of atoms will decay in a predictable manner, but individual atoms decay randomly.
Mathematically, if \(N(t)\) is the number of excited atoms at time \(t\), the relationship can be written as: \[N(t) = N(0)e^{-t/\tau}\] where \(\tau \) is the characteristic decay time or mean lifetime of the excited state.
Heisenberg uncertainty principle
The Heisenberg uncertainty principle is a fundamental concept in quantum mechanics, stating that certain pairs of physical properties cannot be simultaneously known to arbitrary precision. One of these pairs is energy and time.
If we try to determine the exact energy state of an atom, there will be a corresponding uncertainty in the time the atom will remain in that state. This means:
  • We cannot exactly predict the decay time for a single atom.
  • There will always be a degree of uncertainty in both the energy level and the time.
This principle limits our ability to make precise predictions at the quantum level and highlights the inherent probabilistic nature of quantum mechanics.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The Sun has a radius of \(6.96 \times 10^{5} \mathrm{km}\) and a blackbody temperature of \(5780 \mathrm{K}\). Calculate the Sun's luminosity. (Hint: The area of a sphere is \(4 \pi R^{2}\).)

Assume that an object emitting a pure tone of \(440 \mathrm{Hz}\) is on a vehicle approaching you at a speed of \(25 \mathrm{m} / \mathrm{s}\). If the speed of sound at this particular atmospheric temperature and pressure is \(340 \mathrm{m} / \mathrm{s},\) what will be the frequency of the sound that you hear? (Hint: Keep in mind that frequency is inversely proportional to wavelength.)

Astronomers describe certain celestial objects as being redshifted or blueshifted. What do these terms indicate about the objects?

When less energy is radiated from a terrestrial planet, its ________ increases until a new ________ is achieved. a. temperature; equilibrium b. size; temperature c. equilibrium; size d. temperature; size

During a popular art exhibition, the museum staff finds it necessary to protect the artwork by limiting the total number of viewers in the museum at any particular time. New viewers are admitted at the same rate that others leave. Is this an example of static equilibrium or of dynamic equilibrium? Explain.
See all solutions

Recommended explanations on Physics Textbooks

Geometrical and Physical Optics

Read Explanation

Measurements

Read Explanation

Force

Read Explanation

Fluids

Read Explanation

Energy Physics

Read Explanation

Modern Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free